Question

If f(x)=x^4+6, g(x)=x-2 and h(x)= sqrt (x), then f(g(h(x)))=

Please help ASAP I'm really confused with this math problem!!! :(

Answer 1

x^2 + 4x * (3 - sqrt(x)) - 2(5 + sqrt(x))

Explanation:

Firstly let us split this up, we need to first work out what g(h(x)) is:

h(x) = Sqrt(x) so g(h(x)) = g(sqrt(x)) = sqrt(x) - 2

Now to work out f(g(h(x))) = f(sqrt(x) - 2) = (sqrt(x) - 2)^4 + 6

= (sqrt(x) - 2) * (sqrt(x) - 2) * (sqrt(x) - 2) * (sqrt(x) - 2) - 6

= (x - 2 * sqrt(x) + 4) * (x - 2 * sqrt(x) + 4) - 6

= x^2 - 2x * sqrt(x) + 4x - 2x * sqrt(x) + 4x - 8 * sqrt(x) + 4x - 8 * sqrt(x) + 16 - 6

= x^2 - 4x * sqrt(x) + 12x - 16 * sqrt(x) + 10

= x^2 + 4x * (3 - sqrt(x)) - 2(5 + sqrt(x))